Whakaoti i te x-2/x-1+5/3x-4=x+6/x-1

$$\frac { x - 2 } { x - 1 } + \frac { 5 } { 3 x - 4 } = \frac { x + 6 } { x - 1 }$$

Whakaoti mō x

$$x = \frac{27}{19} = 1\frac{8}{19} \approx 1.421052632$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara 1,\frac{4}{3} nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te \left(x-1\right)\left(3x-4\right), arā, te tauraro pātahi he tino iti rawa te kitea o x-1,3x-4.

$$\left(3x-4\right)\left(x-2\right)+\left(x-1\right)\times 5=\left(3x-4\right)\left(x+6\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 3x-4 ki te x-2 ka whakakotahi i ngā kupu rite.

$$3x^{2}-10x+8+\left(x-1\right)\times 5=\left(3x-4\right)\left(x+6\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x-1 ki te 5.

$$3x^{2}-10x+8+5x-5=\left(3x-4\right)\left(x+6\right)$$

Pahekotia te -10x me 5x, ka -5x.

$$3x^{2}-5x+8-5=\left(3x-4\right)\left(x+6\right)$$

Tangohia te 5 i te 8, ka 3.

$$3x^{2}-5x+3=\left(3x-4\right)\left(x+6\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 3x-4 ki te x+6 ka whakakotahi i ngā kupu rite.

$$3x^{2}-5x+3=3x^{2}+14x-24$$

Tangohia te 3x^{2} mai i ngā taha e rua.

$$3x^{2}-5x+3-3x^{2}=14x-24$$

Pahekotia te 3x^{2} me -3x^{2}, ka 0.

$$-5x+3=14x-24$$

Tangohia te 14x mai i ngā taha e rua.

$$-5x+3-14x=-24$$

Pahekotia te -5x me -14x, ka -19x.

$$-19x+3=-24$$

Tangohia te 3 mai i ngā taha e rua.

$$-19x=-24-3$$

Tangohia te 3 i te -24, ka -27.

$$-19x=-27$$

Whakawehea ngā taha e rua ki te -19.

$$x=\frac{-27}{-19}$$

Ka taea te hautanga \frac{-27}{-19} te whakamāmā ki te \frac{27}{19} mā te tango tahi i te tohu tōraro i te taurunga me te tauraro.

$$x=\frac{27}{19}$$